Question

计算：

x2+1

x2-1

-

x-2

x-1

÷

x-2

x

Answer 1

分析：解题关键是先把除法统一为乘法，化简后再算减法．再通分，然后合并同类项再化简即可．

解答：解：

x2+1

x2-1

-

x-2

x-1

÷

x-2

x

=

x2+1

x2-1

-

x-2

x-1

×

x

x-2

=

x2+1

x2-1

-

x

x-1

=

x2+1

(x+1)(x-1)

-

x2+x

(x+1)(x-1)

=

x2+1-x2-x

(x+1)(x-1)

=

1-x

(x+1)(x-1)

=-

1

x+1

故答案为-

1

x+1

．

点评：本题考查分式的混合运算，关键是通分，合并同类项，注意混合运算的运算顺序．